Abstract
In this paper, we analyze the convergence of a finite element method for the computation of transmission eigenvalues and corresponding eigenfunctions. Based on the obtained error estimate results, we propose a multigrid method to solve the Helmholtz transmission eigenvalue problem. This new method needs only linear computational work. Numerical results are provided to validate the efficiency of the proposed method.
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Acknowledgments
X. Ji is supported by the National Natural Science Foundation of China (No. 11271018, No. 91230203) and the Special Funds for National Basic Research Program of China (973 Program 2012CB025904, 863 Program 2012AA01A309), the national Center for Mathematics and Interdisciplinary Science, CAS. J. Sun is supported in part by the National Science Foundation DMS-1016092 and the US Army Research Laboratory and the US Army Research Office under cooperative agreement number W911NF-11-2-0046. H. Xie is supported in part by the National Science Foundations of China (NSFC 91330202, 11001259, 11371026, 11031006, 2011CB309703), the national Center for Mathematics and Interdisciplinary Science, CAS, the President Foundation of AMSS-CAS.
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Ji, X., Sun, J. & Xie, H. A Multigrid Method for Helmholtz Transmission Eigenvalue Problems. J Sci Comput 60, 276–294 (2014). https://doi.org/10.1007/s10915-013-9794-9
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DOI: https://doi.org/10.1007/s10915-013-9794-9